Mathematics Question and Solution
Calculating length PQ.
tana = 12/5
a = atan(12/5)
a = 67.380135052°
b = 180-a
b = 180-67.380135052
b = 112.619864948°
c = ½(b)
c = ½(112.619864948)
c = 56.309932474°
tan56.309932474 = r/d
d = r/(1.5)
tan45 = r/e
e = r
It implies;
d+e = 5
r/(1.5)+r = 5
r+1.5r = 7.5
2.5r = 7.5
r = 3 units.
r is the radius of the circle.
f = 90+a
f = 90+67.380135052
f = 157.380135052°
f is the angle subtending PQ and the radius of the circle.
It implies;
(PQ)² = 2(3)²-2(3)²cos157.380135052
PQ = 5.8834840541 units.
PQ = 5.88 units to 2 decimal places.
